For examples see the attached link.

Poisson regression is about a response that is a count variable. It does not matter what the predictor variables are; they may be continuous or discrete, quantitative or categorical.

The Poisson model assumes that the rate constant* with which the observed events is identical in all samples. This restriction is pretty restrictive. In such processes the variance of the values will happen to be similar to the mean. If you observe this similarity, a Poisson regression is ok. However, usually the assumption of identical rate constants between individuals is not sensible, what usually leads to a variance that is larger than the mean ("overdispesion"). If you obseve this it may be better to use a less restrictive model, and one of the usual choices in this case is the negative binomial model.

*this is the (only) parameter in a Poisson model, mostly called "lamba"

http://www.ncbi.nlm.nih.gov/pubmed/?term=poisson+regression

If you have a continuous outcome (Y) - how much spent on healthcare utilisation it is likely you can use a linear regression model. Depending on the distribution of Y (or strictly the residuals of the model) you might consider a transformation such as a log transformation (given that spend is likely to be positively skewed).

There is no advantage to trying to create a discrete variable (and in any case Poisson is likely to be a poor choice for a discrete model in this case - as you'd want a method that handles over dispersion which is common when the count variable has hidden dependencies - as would likely happen here).

Yes, I overlooked this, and Thom noted this correctly: your response is an amount of money, what is a continuous variable and not a count variable. Therefore a Poisson model is not the right choise. I also think that a standard linear regression model with the log-transformed response will likely be ok.

The amount spent on health care in the last month is a weasel variable.

Are there zeros in your data? If there are, zeros are going to come from two sources:

1. People who spend money on healthcare, but didn't spend any in the last month

2. People who don't spend money on healthcare (because they are healthy, for example)

If this model holds, you will find an excess of zeros. You will need a model that accounts for this. One advantage of zero-inflated Poisson models with robust variance estimation is that they do a pretty good job in cases like this, but I'd check the econometric literature for recommendations.

If there are no zeros in your data, you are still not home and dry, because your data are now zero-truncated. Data like this arise from healthcare billing data. If you don't pay a bill in the month in question, you aren't in the sample but you are in the population.

Again, zero-truncated data has its own methodology, and I'd have a look at the literature in your area.

If excess zeroes are a problem but the distribution of the money spent (from those who did spend money at all) is non-Poisson, then there are other options available. A good overview on this subject is given by Min & Agresti, see

http://www.stat.ufl.edu/~aa/articles/min_agresti_2002.pdf

Zero inflated models might be used, but many times a negative binomial model fits well to zero inflated data and zero inflated models become unnecessarily complex. Hence negative binomial models might be preferred instead.

As a side note, there are zero truncated negative binomial models too.

Mehmet : If I suspect that there's a zero inflation process generating the data, then I feel I've no choice but to model it. Complex often just means realistic.

Jochen : you're a fountain of useful papers – thanks! Although standard Poisson regression has only a single parameter, robust variance estimation allows for overdispersion, making it a very powerful way of attacking skewed data with zeros. 

See this excellent post by Bill Gould : http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/

If you want to apply Poisson regression itself, you can make different categories labelled as  0,1,2,....  depending on the values in various classes.However it is not a proper model.